View Full Version : Fastest way to figure out redraw pot odds

09-25-2005, 11:09 PM
Fairly simple, Hero has some kind of draw, villian has some kind of hand, but when hero makes draw, villian has redraws. How do you work out the redraw math and work it into the total percentage of hero making a hand that is good?

EG: Hero has 56h. Villian has TT. Flop is T 4 7 w/ 2 hearts. Hero has 15 outs twice, which makes him about a 55% in the hand. Villian has a 10 out redraw on the river for two cards however, which will be 20%ish to hit. I know its 42 / 58 from the card player odds thing, but i'd like to know how to work this out quickly.

09-25-2005, 11:31 PM
First of all, a card can only be an out for one player. For example, if T/images/graemlins/heart.gif is still in the deck, it is an out for villain, not hero.

If there are no overlaps, so there are 10 cards that win for villain, 15 cards that win for hero but only if none of the villain's 10 show up; and if none of the 25 cards appear on the turn or river villain wins then:

10*9/2 + 10*35 = 395 times villain gets at least one good card and wins
15*14/2 + 15*20 = 405 times hero gets a good card and villain doesn't, hero wins
20*19/2 = 190 times neither player gets a good card and villain wins

That adds up to 990, the number of possible combinations of turn and river cards. 405 of them win for hero and 585 win for villain. The exact answer is either 399 (4 or 7 on the flop is not a heart) and 417 (T on the flop is not a heart) wins for hero.

09-26-2005, 01:15 AM
What is the math you are showing? I understand it but not wear the numbers in the first bit are coming from :

10*9/2 + 10*35 = 395 times villian gets at least one good card
the 10 is obviously number of outs, the 9/2 is what? and the 35?

09-26-2005, 09:31 PM
10 is the number of outs.

10*9/2 is the number of ways villain can get two outs.

10*35 is the number of ways the villain can get one out and one non-out.

It's tempting to say there are 45 outstanding cards, so villain can get any of 10 outs times any of the 44 other cards for 440 combinations. But this double counts the 45 combinations with two outs.

When the two cards are indistinguishable, as with two outs, you have to divide by 2 to avoid double counting. When the two cards are distinguishable, as in one out and one non-out, you don't divide by 2.